In a parallel universe system (previously discussed here and here), portals are mechanical door frames that, when activated, cause a copy of your universe to appear on the other side. You and your parallel-universe doppelganger initially mirror each other's actions, but after some small amount of time, due to quantum fluctuations (don't worry about it), the two universes de-sync. After that point, there's just two of every object, but the two universes can evolve in different trajectories.
The question is: what's the best-possible naming scheme for these parallel universes? Traditionally in stories with multiple universes, this is not explained ("I'm from Earth 187"). However, simply calling the Nth universe we come across "Earth N" isn't going to work in this case. Here's why.
Every time you make a portal, you not only duplicate the current universe, but all other existing universes. After all, if you have a portal you set up last week in your basement (let's say, to an "Earth 2"), and you open a new portal in your attic to an Earth 3, then of course your house in Earth 3 has a basement with a portal in there that leads to an Earth 4. Note that this 4th universe doesn't have a portal in their attic, because you set the attic portal up after the basement portal de-synced.
(Please, please don't argue in your answer that the portals don't actually work this way. This is easy to misunderstand, so if you think every portal needs to connect to the same universe, or it goes on infinitely, or some other reason why the whole premise is flawed, just don't write an answer. It's not helpful.)
In summary, every time any portal turns on, the number of universes doubles. I considered giving every universe an ID, and then when a new portal opens, adding a 0 to the end of every ID on one side of the portal and a 1 to the end of every ID on the other side. However, an ID with a number of digits equal to the number of portals is way too long and cumbersome to use in day-to-day life. And if you shorten it by converting from binary to decimal, then every time someone opens a portal, everyone in every universe has to memorize a completely new set of digits.
Note that the arrangement of portals isn't always a straight line, either, so numbering them from 1 to 2^N is out. For instance, you could open a third portal in your living room to Earths 5 through 8. Now Earth 1 connects directly to Earth 2, Earth 3, and Earth 5, while all other universes are more than one portal away from Earth 1. An ideal naming system would give connected worlds similar names.
To summarize, a perfect naming system would be
- Robust (every universe's name should not change drastically when a new portal opens)
- Concise (I won't give a character limit, since maybe keywords work better or something, but it needs to be memorizable when there are, say, 20 open portals, or roughly a million total worlds)
- Local (every universe's name should be similar to the names of the other universes that it's connected to).
A fully-perfect solution probably doesn't exist, and it's easy to come up with solutions that do extremely well on 1 out of the above 3 criteria. What I really want is a naming convention that does pretty well on all 3 counts.